Giant Atomic Swirl in Graphene Bilayers with Biaxial Heterostrain.

The study of moiré engineering started with the advent of van der Waals heterostructures, in which stacking 2D layers with different lattice constants leads to a moiré pattern controlling their electronic properties. The field entered a new era when it was found that adjusting the twist between two graphene layers led to strongly-correlated-electron physics and topological effects associated with atomic relaxation. A twist is now routinely used to adjust the properties of 2D materials. This study investigates a new type of moiré superlattice in bilayer graphene when one layer is biaxially strained with respect to the other-so-called biaxial heterostrain. Scanning tunneling microscopy measurements uncover spiraling electronic states associated with a novel symmetry-breaking atomic reconstruction at small biaxial heterostrain. Atomistic calculations using experimental parameters as inputs reveal that a giant atomic swirl forms around regions of aligned stacking to reduce the mechanical energy of the bilayer. Tight-binding calculations performed on the relaxed structure show that the observed electronic states decorate spiraling domain wall solitons as required by topology. This study establishes biaxial heterostrain as an important parameter to be harnessed for the next step of moiré engineering in van der Waals multilayers.

Twists and the Electronic Structure of Graphitic Materials.

We analyze the effect of twists on the electronic structure of configurations of infinite stacks of graphene layers. We focus on three different cases: an infinite stack where each layer is rotated with respect to the previous one by a fixed angle, two pieces of semi-infinite graphite rotated with respect to each other, and finally a single layer of graphene rotated with respect to a graphite surface. In all three cases, we find a rich structure, with sharp resonances and flat bands for small twist angles. The method used can be easily generalized to more complex arrangements and stacking sequences.

Electrostatic effects, band distortions, and superconductivity in twisted graphene bilayers.

Bilayer graphene twisted by a small angle shows a significant charge modulation away from neutrality, as the charge in the narrow bands near the Dirac point is mostly localized in a fraction of the Moiré unit cell. The resulting electrostatic potential leads to a filling-dependent change in the low-energy bands, of a magnitude comparable to or larger than the bandwidth. These modifications can be expressed in terms of new electron-electron interactions, which, when expressed in a local basis, describe electron-assisted hopping terms. These interactions favor superconductivity at certain fillings.

Edge Modes and Nonlocal Conductance in Graphene Superlattices.

We study the existence of edge modes in gapped moiré superlattices of graphene monolayer ribbons on a hexagonal boron nitride substrate. We find that the superlattice bands acquire finite Chern numbers, which lead to a valley Hall effect. The presence of dispersive edge modes is confirmed by calculations of the band structure of realistic nanoribbons using tight binding methods. These edge states are only weakly sensitive to disorder, as short-range scattering processes lead to mean free paths of the order of microns. The results explain the existence of edge currents when the chemical potential lies within the bulk superlattice gap, and offer an explanation for existing nonlocal resistivity measurements in graphene ribbons on boron nitride.